Theorem 5p3e8

Description: 5 + 3 = 8. (Contributed by NM, 11-May-2004)

	Ref	Expression
Assertion	5p3e8	$$⊢5+3=8$$

Proof

Step	Hyp	Ref	Expression
1		df-3	$$⊢3=2+1$$
2	1	oveq2i	$$⊢5+3=5+2+1$$
3		5cn	$$⊢5\in ℂ$$
4		2cn	$$⊢2\in ℂ$$
5		ax-1cn	$$⊢1\in ℂ$$
6	3 4 5	addassi	$$⊢5+2+1=5+2+1$$
7	2 6	eqtr4i	$$⊢5+3=5+2+1$$
8		df-8	$$⊢8=7+1$$
9		5p2e7	$$⊢5+2=7$$
10	9	oveq1i	$$⊢5+2+1=7+1$$
11	8 10	eqtr4i	$$⊢8=5+2+1$$
12	7 11	eqtr4i	$$⊢5+3=8$$